Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

weibull_damage.mw
i have weibull plot...and i want to get size and shpae parametr...how can i get ...parameters .i don't know how to perform linear regression to get these parameters in maple..please help

I noticed that in a legend with:

  1. Three elements
  2. linestyle = [solid, longdash, dash]
  3. thickness = [4, 4, 4]

The three different linestyles are distinguishable in the plots (of course, since the curves span the whole plot area) but indistinguishable in the legend box. Since the legend box is too narrow, the symbols for a solid line, a longdash line, and a dash line are equivalent, resulting in confusion regarding which element is associated to each linestyle. Note that I don't want to use three different colors to achieve that or change my font sizes

  1. How can I "show more" of the linestyle in the legend box? "Longer" line symbols in the legend box would allow to dinstinguish a solid from a longdash from a dash even when all three are quite thick.
  2. Alternatively, can I reduce the thickness of the line symbols in the legend box (leaving unaltered the thickness of the lines in the actual plot)? "Slimmer" line symbols in the legend box would allow to dinstinguish a solid from a longdash from a dash even when all three are quite short.

Can_I_change_the_location_of_the_color_bar_caption_in_Maple_2024.mw

In Maple 2024,

can I change the location of the color bar caption in Maple 2024? It conflicts with the color bar labels sometimes. See the attached maple sheet for an example.

I am using fsolve() to solve a highly nonlinear system of 6 equations in 6 variables: lambda_d1, lambda_i1, lambda_d2, lambda_i2, lambda_d3, lambda_i3.

fsolve() doesn't "solve"! I usually help fsolve() with some initial conditions and with the expected signs of the solution but in this case it's not enough. I noticed that if I comment out the expected signs line (that is, if I don't impose my 6 lambdas to be strictly positive), the fsolve() works.
How do I help fsolve() to pin down only positive solutions at each iteration? I have no reasons to believe that there aren't any positive solutions for all 6 lambdas...

Worksheet: fsolve_help.mw

thank you.

can we express 'X' in terms of 'L'? i.e., X = (some const)*L XintoL.mw

Hello,
can anyone tell me why the following expression evaluates to false in Maple?

restart;
evalb(sin(x + y) = sin(x)*cos(y) + cos(x)*sin(y));                 
false

The underlying term "sin(x+y) = sin(x) cos(y) + cos(x) sin(y)" is one of the addition theorems that have been proven to be valid.

Thank you in advance for your answer.

Best regards
Jan

I tried to solve a ODE system using rkf45 with shooting technique. But I have a lot of errors. How to resolve this...

See the attachment: Shoot_Blasius.mw

I have some long expressions that would be more readable if common sections were substituted out. There are many sets of radicals often stacked inside each other.  The other one is (a*x..........) I see repeated in some other expressions. indets is good, but is there a way to use it to select  (a*x..........) types
At these eexpressions are returned from procdures would probably put them in an array/table with their substitution components. 
I dont need to substitute everything. What I have done below is reasonable for reading and seeing the structure.

What would be a good approact here?

restart

 

18*x^2+21*x*y+7*y^2-29*x-37*y-56

(1)

vals:=[a=18,b=21,c=7,d=-29,e=-37,f=-56]

[a = 18, b = 21, c = 7, d = -29, e = -37, f = -56]

(2)

vars[1]:=x:vars[2]:=y:

eqn:= 8*(2*((a^2-2*a*c+b^2+c^2)*(4*a*c*f-a*e^2-b^2*f+b*d*e-c*d^2)^2)^(1
                /2)+(-8*a*f+2*d^2)*c^2+(8*a^2*f-2*a*d^2+2*a*e^2+2*b^2*f-2*b*d*e)*c-2*a^2*e^2-2*
                a*b^2*f+2*a*b*d*e)^(1/2)*(a*c-1/4*b^2)/(4*a*c-b^2)^2*(vars[1]-(1/4*b*e-1/2*c*d)/(a*c-\
                1/4*b^2))-8*csgn((4*a*c*f-a*e^2-b^2*f+b*d*e-c*d^2)*(Complex(1)*a+Complex(-1)*c-
                b))*(a*c-1/4*b^2)*(2*((a^2-2*a*c+b^2+c^2)*(4*a*c*f-a*e^2-b^2*f+b*d*e-c*d^2)^2)^
                (1/2)+(8*a*f-2*d^2)*c^2+(-8*a^2*f+2*a*d^2-2*a*e^2-2*b^2*f+2*b*d*e)*c+2*a^2*e^2+
                2*a*b^2*f-2*a*b*d*e)^(1/2)/(4*a*c-b^2)^2*(vars[2]-(-1/2*a*e+1/4*b*d)/(a*c-1/4*b^2))

8*(2*((a^2-2*a*c+b^2+c^2)*(4*a*c*f-a*e^2-b^2*f+b*d*e-c*d^2)^2)^(1/2)+(-8*a*f+2*d^2)*c^2+(8*a^2*f-2*a*d^2+2*a*e^2+2*b^2*f-2*b*d*e)*c-2*a^2*e^2-2*a*b^2*f+2*a*b*d*e)^(1/2)*(a*c-(1/4)*b^2)*(x-((1/4)*b*e-(1/2)*c*d)/(a*c-(1/4)*b^2))/(4*a*c-b^2)^2-8*csgn((4*a*c*f-a*e^2-b^2*f+b*d*e-c*d^2)*(I*a-I*c-b))*(a*c-(1/4)*b^2)*(2*((a^2-2*a*c+b^2+c^2)*(4*a*c*f-a*e^2-b^2*f+b*d*e-c*d^2)^2)^(1/2)+(8*a*f-2*d^2)*c^2+(-8*a^2*f+2*a*d^2-2*a*e^2-2*b^2*f+2*b*d*e)*c+2*a^2*e^2+2*a*b^2*f-2*a*b*d*e)^(1/2)*(y-(-(1/2)*a*e+(1/4)*b*d)/(a*c-(1/4)*b^2))/(4*a*c-b^2)^2

(3)

length(eqn)

962

(4)

simplify(eval(eqn,vals))

(4/567)*(9*x+53)*(-63382+5762*562^(1/2))^(1/2)+(4/1323)*(-21*y+241)*(63382+5762*562^(1/2))^(1/2)

(5)

indets(eqn)

{a, b, c, d, e, f, x, y, ((a^2-2*a*c+b^2+c^2)*(4*a*c*f-a*e^2-b^2*f+b*d*e-c*d^2)^2)^(1/2), (2*((a^2-2*a*c+b^2+c^2)*(4*a*c*f-a*e^2-b^2*f+b*d*e-c*d^2)^2)^(1/2)+(-8*a*f+2*d^2)*c^2+(8*a^2*f-2*a*d^2+2*a*e^2+2*b^2*f-2*b*d*e)*c-2*a^2*e^2-2*a*b^2*f+2*a*b*d*e)^(1/2), (2*((a^2-2*a*c+b^2+c^2)*(4*a*c*f-a*e^2-b^2*f+b*d*e-c*d^2)^2)^(1/2)+(8*a*f-2*d^2)*c^2+(-8*a^2*f+2*a*d^2-2*a*e^2-2*b^2*f+2*b*d*e)*c+2*a^2*e^2+2*a*b^2*f-2*a*b*d*e)^(1/2), csgn((4*a*c*f-a*e^2-b^2*f+b*d*e-c*d^2)*(I*a-I*c-b))}

(6)

Subs:=[((a^2 - 2*a*c + b^2 + c^2)*(4*a*c*f - a*e^2 - b^2*f + b*d*e - c*d^2)^2)=A^2,
         (-8*a*f + 2*d^2)*c^2 + (8*a^2*f - 2*a*d^2 + 2*a*e^2 + 2*b^2*f - 2*b*d*e)*c - 2*a^2*e^2 - 2*a*b^2*f + 2*a*b*d*e=B^2,
           f*b^3 - b^2*d*e - (-(-4*c*f + e^2)*a - c*d^2)*b=C]:

eqn1:=simplify(eqn,Subs)

(-8*csgn(C+((1/2)*I)*B^2)*(-(1/4)*y*b^2-(1/4)*b*d+a*(y*c+(1/2)*e))*(-B^2+2*(A^2)^(1/2))^(1/2)+8*(B^2+2*(A^2)^(1/2))^(1/2)*(-(1/4)*b^2*x-(1/4)*b*e+c*(a*x+(1/2)*d)))/(4*a*c-b^2)^2

(7)

Subsnumeric:=eval(Subs,vals)

[74635047712 = A^2, -253528 = B^2, 242004 = C]

(8)

simplify(eval(eqn1,[(rhs=lhs)~(Subsnumeric)[],vals[] ]))

(4/567)*(9*x+53)*(-63382+5762*562^(1/2))^(1/2)+(4/1323)*(241-21*y)*(63382+5762*562^(1/2))^(1/2)

(9)
 

 

Download 2024-05-27_Q_Pick_Apart_an_Expression.mw

I was trying to solve a system of eight cubic equations, with eight variables. Note that the particular solutions should exist and my goal is to find all  possible solutions using solve. However, when executing, the solve keeps running for a whole day and did not throw any results. I also set the parameter infolevel[solve] to be 3 and find out that it is stuck in the step "GroebnerBasis: computing a factored plex basis using Groebner[Solve]". Can anyone tell me how to deal with that? Here's the Maple file.

solve_test.mw

This is still a  starting procedure and let's see what can be added?

restart;
# Define the procedure to draw a cylinder along the x-axis and a specifically positioned plane
CylinderAndPlane := proc(r, h, alpha_deg, beta_deg, P, axis_length)
    local alpha, beta, cylinder, plane, pointPlot, display, nx, ny, nz, px, py, pz, annotations, plane_type, titleStr, grafiek;  # Added: titleStr
    uses plots, LinearAlgebra;  
    # Convert angles from degrees to radians
    alpha := alpha_deg * Pi / 180;
    beta := beta_deg * Pi / 180;

    # Determine the normal vector based on angles
    nx := cos(alpha) * sin(beta);
    ny := sin(alpha) * sin(beta);
    nz := cos(beta);

    # Point P is directly used as given coordinates
    px, py, pz := op(P);

    # Cylinder along the x-axis
    cylinder := plots:-implicitplot3d(y^2 + z^2 = r^2, x = 0 .. h, y = -r .. r, z = -r .. r, style = surface, color = "LightBlue", transparency = 0.5);

    # Determine the type of plane based on angles alpha and beta
    if beta_deg = 90 then
        plane_type := "yz";
        plane := plots:-implicitplot3d(x = px, x = px - 10 .. px + 10, y = -axis_length .. axis_length, z = -axis_length .. axis_length, style = surface, color = "Yellow", transparency = 0.5);
    elif alpha_deg = 90 and beta_deg = 0 then
        plane_type := "xz";
        plane := plots:-implicitplot3d(y = py, x = -axis_length .. axis_length, y = py - 10 .. py + 10, z = -axis_length .. axis_length, style = surface, color = "Green", transparency = 0.5);
    elif beta_deg = 0 then
        plane_type := "xy";
        plane := plots:-implicitplot3d(z = pz, x = -axis_length .. axis_length, y = -axis_length .. axis_length, z = pz - 10 .. pz + 10, style = surface, color = "Blue", transparency = 0.5);
    else
        plane_type := "arbitrary";
        plane := plots:-implicitplot3d(nx * (x - px) + ny * (y - py) + nz * (z - pz) = 0, x = -axis_length .. axis_length, y = -axis_length .. axis_length, z = -axis_length .. axis_length, style = surface, color =            "Red", transparency = 0.7);
    end if;

    # Mark point P
    pointPlot := plots:-pointplot3d([px, py, pz], symbol = solidcircle, symbolsize = 10, color = "Red");

    # Create dynamic title - New
    titleStr := cat("Plane: ", plane_type, "\nAlpha: ", sprintf("%.2f", alpha_deg), " deg\nBeta: ", sprintf("%.2f", beta_deg), " deg\nPoint: [", sprintf("%.2f", P[1]), ", ", sprintf("%.2f", P[2]), ", ", sprintf("%.2f", P[3]), "]");

    # Display everything together - Modified: titleStr added in the display function
    grafiek := plots:-display(cylinder, plane, pointPlot, axes = normal, scaling = constrained, labels = ["x", "y", "z"], title = titleStr);

    return grafiek;
end proc:

# Example call to the procedure with coordinates of P and setting the axis length
# Alpha and Beta are now angles in degrees, P is a list of coordinates, axis_length is the length of the coordinate axes
CylinderAndPlane(15, 50, 0, 90, [15, 5, 5], 30);  # For yz-plane
#CylinderAndPlane(5, 15, 90, 0, [5, 5, 5], 10);  # For xz-plane
#CylinderAndPlane(5, 15, 0, 0, [5, 5, 5], 10);   # For xy-plane
#CylinderAndPlane(5, 55, 45, 45, [5, 5, 5], 10); # For arbitrary plane

 
 

 

Download maple_primes_-doorsnijdingsvlak_solids_procedureDEF.mw

How do I calculate and plot an Orthogonal Trajectory on Maple 2024?

Here's the equation of the contour lines:

x*y^2 - x^2 - y^2 = k

I need to make it pass through a precise point on my contour lines graph, and everything I do doesn't seem to work.

I have tried to understand why ODESteps cannot find a solution for cases where an ODE can separated into a polynomial expression and an ODE.

or example, when I trace like this

restart;
trace(Student:-ODEs:-ODESteps:-ModuleApply);
printlevel:=10;
Student:-ODEs:-ODESteps:-ModuleApply(x*(diff(y(x), x)) = 0);
printlevel:=1

trace is tracing an unknown procedure

and not showing any further details of this procedure.
What unknow function/procedure is traced?

Can, in this particular case, the message "Cannot compute integral"   be traced (it’s not an error message, which are traceable).

I have tried to increase printlevel which reveals some unkown procedures but did not get down to this one. Hence my questions.

sol := y = -3283/4253 - (3283*x)/4253, How can I determine the value of the coefficient of x?
How can I take the value of the coefficient of x? Thank you.

At here https://mathematica.stackexchange.com/questions/297104/how-can-i-convert-a-list-containing-three-points-and-its-equation-passing-three is discussing about "How can I convert a list containing three points and its equation passing three points to text file?" With mylist

mylist := [[[-12, 2, -1], [-11, 1, -5], [-10, -2, 3], 10*x + 6*y + z + 109 = 0], [[-12, 2, -1], [-11, 1, -5], [-10, 6, 3], 2*x - 2*y + z + 29 = 0], [[-12, 2, -1], [-11, 1, -5], [-9, 5, -7], 3*x - y + z + 39 = 0]]

How can I get the LaTeX file like this?

\documentclass[12pt,a4paper]{article}
\usepackage[letterpaper,margin=1.2in]{geometry}
\usepackage{enumitem}
\begin{document}
\begin{enumerate}[label=\arabic*)]
\item $A(-12; 2; -1)$,\quad $B(-11; 1; -5)$,\quad $C(-10; -2; 3)$,\quad $(P) : 10 x+6 y+z+109=0$
\item $A(-12; 2; -1)$,\quad $B(-11; 1; -5)$,\quad $C(-10; 6; 3)$,\quad $(P) : 2 x-2 y+z+29=0$
\item $A(-12; 2; -1)$,\quad $B(-11; 1; -5)$,\quad $C(-9; 5; -7)$,\quad $(P) : 3 x-y+z+39=0$
\end{enumerate}
\end{document}


 

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